To solve this question, we need to focus on the relationship between a function \( F(x) \) and its inverse \( F^{-1}(x) \). One key property of functions and their inverses is that if a point \((a, b)\) is on the graph of the function \( F(x) \), then the point \((b, a)\) must be on the graph of the inverse function \( F^{-1}(x) \).
Given that the point \((8, -2)\) is on the graph of \( F(x) \), to find the corresponding point on the graph of \( F^{-1}(x) \), we simply switch the coordinates. That means the point on the graph of \( F^{-1}(x) \) would be \((-2, 8)\).
Here's a step-by-step breakdown:
1. Start with the point \((8, -2)\) on the graph of \( F(x) \).
2. Since \( F^{-1}(x) \) undoes the effect of \( F(x) \), we swap the x-coordinate and the y-coordinate of \((8, -2)\).
3. Swapping the coordinates gives us the point \((-2, 8)\).
Thus, the point that must be on the graph of the inverse function \( F^{-1}(x) \) is \((-2, 8)\).
Therefore, the correct answer is:
B. [tex]\((-2, 8)\)[/tex]
